Research on mesoscopic inductance–capacitance coupling circuit employing an unitary operator and the IWOP technique

Employing a special unitary operator and the virtue of the technique of integration within an ordered product (IWOP), we research on the quantum effects for an inductance–capacitance coupling double L–C circuit. It is found that it is convenient to research on the mesoscopic circuit with such an operator. First, eliminating the coupling term of Hamiltonian becomes easier than other methods. Second, the system’s ground state can be easily generalized into a two-mode squeezed state. Thus, the quantum fluctuations of the circuit and the variances of current in each loop are calculated, the charge-current uncertainty relation is revealed. As a result, both the uncertainty relation and fluctuation of the current in each loop become larger when [Formula: see text] is larger or [Formula: see text] is smaller.

New approach to generating functions of single- and two-variable even- and odd-Hermite polynomials and applications in quantum optics

Using the IWOP technique and completeness of representation, we obtain the integral expressions of single- and two-variable Hermite polynomials. Based on this, we further derive the generating functions of single- and two-variable even- and odd-Hermit polynomials. This method seems more concise and direct. In addition, some applications such as deriving new formula and constructing new two-mode quantum states are discussed. It is found that two-variable Hermite polynomials excitation can used to produce entangled coherent states.

SOLVING MASTER EQUATION FOR CALDEIRA–LEGGETT MODEL BY VIRTUE OF THE THERMO ENTANGLED STATE REPRESENTATION AND THE IWOP TECHNIQUE

In the present work, the exact formal solution of the Caldeira–Leggett quantum master equation for the reduced density matrix of an oscillator is obtained by virtue of the thermo entangled state representation and the technique of integration within an ordered product (IWOP) of operators. Also, the solution for high temperature approximation is derived. When the initial state is a coherent state, it will evolve into a displaced-squeezed chaotic state (a mixed state) which shows that decoherence is involved in the Caldeira–Leggett equation due to the interactions between the system and environment.